Removing Pillar Tap and faucet

Hi all,

I'm completely inexperienced at this, but my kitchen taps are ancient, and the water has started dripping. Rather than just change the washer, I want to change the entire thing to a mixer tap that supports two holes. I think I've figured most of it out except for the part where I actually remove the old faucet. Most websites show them held in place with a mounting nut which mine doesn't have.

I'm not sure, but does it look like a basin wrench would be the tool to remove mine?...

Removing Pillar Tap and faucet